Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x + 4$ and $ BC = 6x + 18$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x + 4} = {6x + 18}$ Solve for $x$ $ 2x = 14$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({7}) + 4$ $ BC = 6({7}) + 18$ $ AB = 56 + 4$ $ BC = 42 + 18$ $ AB = 60$ $ BC = 60$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {60} + {60}$ $ AC = 120$